Abstract
In this chapter we use a numerical technique to analyze the onset of Marangoni convection in a horizontal layer of electrically conducting fluid heated from below and cooled from above in the presence of a uniform vertical magnetic field. The top surface of a fluid is deformably free and the bottom boundary is rigid and free-slip. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and the latter is found to be critically dependent on the Hartmann, Crispation, and Bond numbers. In particular, we present an example of a situation in which there is competition between modes at the onset of convection.
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Arifin, N.M., Rosali, H. (2009). On competition between modes of the onset of Marangoni convection with free-slip bottom under magnetic field. In: Mastorakis, N., Sakellaris, J. (eds) Advances in Numerical Methods. Lecture Notes in Electrical Engineering, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76483-2_3
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DOI: https://doi.org/10.1007/978-0-387-76483-2_3
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